Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

Florentin M\"unch; Matthias Keller

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Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians

Matthias Keller, Florentin Münch

Differential Geometry · Submitted 26 Jul 2018

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The authors' main claim In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption.

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arXiv ID1807.10181 (version 2)

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CitationFlorentin M\"unch, Matthias Keller. "Gradient estimates, Bakry-Emery Ricci curvature and ellipticity for unbounded graph Laplacians." arXiv:1807.10181 (2018). https://pith.science/paper/BYRGOBGF

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In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption.	contribution 0.68	0.96	0.91	asserted 1.00
s1	As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.	contribution 0.91	0.91	0.09	asserted 0.85

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In this article, we prove gradient estimates under Bakry-Emery curvature bounds for unbounded graph Laplacians which satisfy an ellipticity assumption. As applications, we study completeness and finiteness of stochastically complete graphs under Bakry-Emery curvature bounds.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities
math.DG 2026-07 conditional novelty 8.0 of 10

Connected bounded-degree graphs satisfying CD(0,∞) for the unnormalised Laplacian are volume doubling and satisfy scale-invariant L² Poincaré inequalities with dilation two.
Stochastic completeness of graphs: bounded Laplacians, intrinsic metrics, volume growth and curvature
math.MG 2020-09 conditional

A survey of stochastic completeness on graphs, centered on intrinsic metrics, volume growth, and curvature criteria, with no new theorems.

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5 arXiv papers cite this in 6 sentences

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Compares with it 1 paper

Nor do the pointwise semigroup reverse Poincaré estimates of [ref] , the pseudo-Poincaré estimate in [ref] , the global Buser inequalities in [ref] , or the conical-curvature global inequality in [ref] furnish the required localisation on arbitrary balls.

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities · The local Poincaré problem · 0.89

Cites it as background 3 papers

For the classical condition itself, Lin and Liu identified the bounded-generator equivalence with heat-semigroup gradient and variance inequalities [ref] ; Keller and Münch obtained related semigroup characterisations for unbounded graph Laplacians under suitable domain and ellipticity hypotheses [ref] .

Nonnegative Bakry--\'Emery Curvature on Bounded-Degree Graphs Implies Volume Doubling and Poincar\'e Inequalities · Curvature conditions and discrete Li–Yau theories · 0.92
Curvature-dimension inequalites in the discrete setting, in particular for (locally) finite graphs are studied intensively ( [ref] ).

Curvature-dimension inequalities for non-local operators in the discrete setting · Introduction and main results · 0.95
There are a growing number of articles investigating this theory, see e.g., [ref] .

Bakry-\'Emery curvature on graphs as an eigenvalue problem · Introduction and statements of result · 0.94

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